The Interaction between Fuzzy Subsets and Groupoids

Title
The Interaction between Fuzzy Subsets and Groupoids
Author
김희식
Issue Date
2014-04
Publisher
HINDAWI PUBLISHING CORPORATION, 410 PARK AVENUE, 15TH FLOOR, #287 PMB, NEW YORK, NY 10022 USA
Citation
?e Scientific World Journal, Volume 2014, Article ID 246285, 6 pages
Abstract
We discuss properties of a class of real-valued functions on a set X-2 constructed as finite (real) linear combinations of functions denoted as [(X, *); mu], where (X, *) is a groupoid (binary system) and mu is a fuzzy subset of X and where [(X., *); mu] (x, y) := mu (x * y) - min {mu(x), mu(y)}. Many properties, for example, mu being a fuzzy subgroupoid of (X, *), can be restated as some properties of [(X, *); mu]. Thus, the context provided opens up ways to consider well-known concepts in a new light, with new ways to prove known results as well as to provide new questions and new results. Among these are identifications of many subsemigroups and left ideals of (Bin (X); square) for example.
URI
https://www.hindawi.com/journals/tswj/2014/246285/abs/http://hdl.handle.net/20.500.11754/51682
ISSN
1537-744X
DOI
10.1155/2014/246285
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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